Recently, the anti-eavesdropper (anti-EVE) technique has been well explored in the literature. However, the constant appearance of EVEs was generally assumed. In other words, these works focused on how to escape from being overheard rather than designing a complete transmission scheme with random appearances of EVEs. Thus, in this paper, we take the random appearances into consideration when designing a cooperative transmission scheme in the cognitive radio network using the anti-EVE cluster beamforming (CB) strategy. When EVE is not observed, the proposed cooperative scheme based on the fair three-stage Stackelberg (FTS) game is carried out; otherwise, the conventional CB cooperative scheme without eavesdropper's channel state information is executed. In the FTS game, the cluster of SUs first determines the transmission power to help PU for packet transmissions. Afterwards, PU can also adjust its willingness of sharing transmission time. To avoid extremely selfish time allocation by PU, a referee can make a fair judgement on the time sharing based on the minimization of the difference between PU's and SUs' utility functions. Compared with the conventional method, the superior performance in the sum transmission rates and power efficiency are proved by simulation results.